FIZIKA A 15 (2006) 2 , 91-112

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Department of Physics, Faculty of Education, University of Maribor,
Koroška cesta 160, SI-2000 Maribor, Slovenia
E-mail address:

Received 25 October 2004;  Accepted 12 July 2006
Online 1 December 2006

This article is written for undergraduate students and teachers who would like to get familiar with basic nonlinear time series analysis methods. We present a step-by-step study of a simple example and provide user-friendly programs that allow an easy reproduction of presented results. In particular, we study an artificial time series generated by the Lorenz system. The mutual information and false nearest neighbour method are explained in detail, and used to obtain the best possible attractor reconstruction. Subsequently, the times series is tested for stationarity and determinism, which are both important properties that assure correct interpretation of invariant quantities that can be extracted from the data set. Finally, as the most prominent invariant quantity that allows distinguishing between regular and chaotic behaviour, we calculate the maximal Lyapunov exponent. By following the above steps, we are able to convincingly determine that the Lorenz system is chaotic directly from the generated time series, without the need to use the differential equations. Throughout the paper, emphasis on clear-cut guidance and a hands-on approach is given in order to make the reproduction of presented results possible also for undergraduates, and thus encourage them to get familiar with the presented theory.

PACS numbers: 01.50.-i, 05.45.Tp
UDC 530.182

Keywords: nonlinear time series analysis, physics education

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